This paper reviews the existing developments of adaptive methods of sparse adaptive filters for the identification of sparse impulse response in both network and acoustic echo cancellation from the last decade. A variety of different architectures and novel training algorithms have been proposed in literature. At present most of the work in echo cancellation on using more than one method. Sparse adaptive filters take the advantage of each method and showing good improvement in the sparseness measure performance. This survey gives an overview of existing sparse adaptive filters mechanisms and discusses their advantages over the traditional adaptive filters developed for echo cancellation.